In cylindrical gear units the aim is to bring about an engagement between the various toothed wheels in the gear unit, which engagement is, as far as possible, free of backlash. However, due to manufacturing tolerances of the components of the gear unit, it is practically impossible to bring about a complete freedom from backlash while at the same time ensuring that too high loads, as a result of too hard an engagement between the gear wheels, do not occur. In addition, a variation of the engagement of teeth is obtained as a result of the thermal expansion if the components of the gear unit are manufactured from materials having different coeffients of thermal expansion, which is often the case; for example a steel gear wheel and a light metal gear housing. Within certain fields of application, for example cylindrical gear units which are used in industrial robots and the like for turning parts thereof, however, an engagement without backlash is required in order to obtain the desired high precision in the positioning of the parts. It has therefore been proposed previously to mount one of the shafts in the gear unit with a certain resilience, enabling it to move away somewhat from the other shaft to reduce the stresses in the case of too hard an engagement (cf. patent publications GB No. 1,237,161, GB No. 1,375,214, DE No. 1,450,712 and EP No. 63,702). However, these known arrangements are relatively complicated and hence expensive, and furthermore they are space demanding.